So Sauron had to trick the elves/Celebrimbor into making tainted rings for him. The reason he couldn't just cut out the middle man and make them himself, using his fair physical form, was because........?

1 Answer
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First, Sauron may not have known how to make rings of power. When the project started, no one knew how. Think of ring-making as a long R&D process where smart people work for a very long time figuring out how to make them.

While Sauron was a Maiar, there's no hint anywhere that the Maiar (or even the Valar) were any smarter than people. More powerful, yes. Had more factual knowledge of hidden things, yes. But they weren't smarter. Ring-making was difficult and needed to be figured out.

When Gandalf talked about the rings of power and Gollum, he mentions that there were lesser rings of power which were early essays in the craft and which did not prolong the wearer's life. This supports the theory that ring-making was and art which was discovered over time rather than a technique learned from Sauron.

Sauron (who had a knack for it -- wasn't he one of Aule's Maiar in the beginning?) had some ideas the elves lacked and maybe had some insights into the supernatural parts of Arda, but needed the elves and Celebrimbor (who seems to have been very bright) in particular to work out how to make rings of power.

Once they had done so, Sauron used the same techniques and his special malice and power to produce the One Ring.

The second possibility is that Sauron did know how to make rings of power, but wanted to control the Elves and needed them to make their own rings for that to happen. (Either because those rings would then have more power over them or because they would never wear rings they didn't make themselves.) So he helped them learn the craft and then used the backdoor he installed in the technique to take control using the One Ring.

Both seem possible and I don't know of evidence for or against either.

The fact that neither Gil-Galad or Galadriel trusted 'Annatar' does give some support to the second idea. They were willing to take Rings Celebrimbor gave them (and which happened to be the only three Celebrimbor worked on by himself), but they probably would not have even given Sauron the chance.
– suchiuomizuDec 23 '17 at 23:44